Airplane Seating

Puzzle: Leon Lin sent me this great puzzle: 100 people are in line, boarding an airplane with 100 seats, one at a time. They are in no particular order. The first person has lost his boarding pass, so he sits in a random seat. The second person does the following:

  1. Goes to his seat (the one it says to go to on the boarding pass).
  2. If unoccupied, sit in it.
  3. If occupied, find a random seat to sit in.

Everyone else behind him does the same. What is the probability that the last person sits in his correct seat?

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